Cone-beam reconstruction from general discrete vertex sets

Addresses the issue of reconstruction of a 3D image from cone-beam projections measured for an arbitrary discrete set of vertex points. "Vertex point" refers to the position of the X-ray source in area CT or to the focal point of the CB collimator in SPECT imaging. The problem of defining a practical data sufficiency condition is investigated and a parameter ε₀ is defined to describe how close a discrete vertex set comes to satisfying Tuy\´s condition. A reconstruction algorithm based on the Radon rebinning method is presented which is capable of near-optimal reconstructions from any discrete vertex set, whether or not it represents a sampled vertex path